Defining parameters
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 12 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(144\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(144, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 132 | 10 | 122 |
Cusp forms | 108 | 10 | 98 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(144, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
144.6.c.a | $2$ | $23.095$ | \(\Q(\sqrt{-2}) \) | \(\Q(\sqrt{-1}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta q^{5}+244q^{13}+239\beta q^{17}+3107q^{25}+\cdots\) |
144.6.c.b | $8$ | $23.095$ | 8.0.\(\cdots\).47 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{2}q^{5}+\beta _{5}q^{7}+\beta _{4}q^{11}+(-2^{5}+\cdots)q^{13}+\cdots\) |
Decomposition of \(S_{6}^{\mathrm{old}}(144, [\chi])\) into lower level spaces
\( S_{6}^{\mathrm{old}}(144, [\chi]) \cong \)